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Differentiable functions of quaternion variables

S. V. Ludkovsky·F. van Oystaeyen
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Abstract

We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quaternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass theorem.

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S. V. Ludkovsky, F. van Oystaeyen. 2002-09-13. Differentiable functions of quaternion variables. https://arxiv.org/abs/math/0209166

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